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Category Theory and Risk Measure

Specen-Berry, Ludovic
(2022)

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SpecenBerryLudovic_31110800_2022.pdf
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Details

Supervisors
Ars, Pierre ; Van der Spiegel, Jan
Faculty
Faculté des sciences
Degree label
Master [120] en sciences actuarielles, à finalité spécialisée
Abstract
This master thesis has been completed at the University catholique de Louvain (UCL) in the fulfillment of the grade of Master in Actuarial Sciences. The subject is an application of the category theory in Actuarial Sciences and more specifically in the context of risk measure theory. First, the classical monetary value measure theory is described and related problematics are introduced: Knightian uncertainty and the determination of an adequate set of minimal axioms for such a risk measure. A generalization of this theory is described in the language of categories and shows how to partially answer the two problematics. The last part is dedicated to provide some of the possible concrete applications of this categorical view of probability spaces, conditional expectation and monetary value measure.